Effective field theory for hydrodynamics without boosts

We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation classical boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. find that, up first order in derivatives, is characterised by thermodynamic equation state and total 29 independent transport coefficients, particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, 17 dissipative. Furthermore, we study spectrum linearised fluctuations around anisotropic equilibrium states non-vanishing fluid velocity. analysis reveals pair sound modes that propagate at different speeds along opposite flow, one charge diffusion mode, two distinct shear perpendicular present these results new hydrodynamic frame linearly stable irrespective symmetry place. provides unified approach for simultaneously treating Lorentzian, Galilean, Lifshitz fluids within framework sets stage future studies non-relativistic intertwined patterns breaking.